Ara es mostren els items 1-7 de 7

• #### Cropping Euler factors of modular L-functions ﻿

(2013-09)
Article
Accés obert
According to the Birch and Swinnerton-Dyer conjectures, if A/Q is an abelian variety, then its L-function must capture a substantial part of the properties of A. The smallest number field L where A has all its endomorphisms ...
• #### Modular forms with large coefficient fields via congruences ﻿

(Springer, 2015-05-01)
Article
Accés obert
We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. ...
• #### On fields of definition of torsion points of elliptic curves with complex multiplication ﻿

(2011-06)
Article
Accés obert
For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of ...
• #### Orders of CM elliptic curves modulo p with at most two primes ﻿

(2010)
Article
Accés restringit per política de l'editorial
Nowadays the generation of cryptosystems requires two main aspects. First the security, and then the size of the keys involved in the construction and comunication process. About the former one needs a di±cult ...
• #### Orders of CM elliptic curves modulo p with at most two primes ﻿

(2006)
Article
Accés obert
We prove the analog of Koblitz conjecture when replacing primes by almost prime numbers and considering elliptic curves with complex multiplication. In other words for infinitely many primes $p$, (given in a quantitative ...
• #### Small primitive roots and malleability of RSA ﻿

(2012)
Text en actes de congrés
Accés obert
In their paper [9], P. Paillier and J. Villar make a conjectur e about the malleability of an RSA modulus. In this paper we present an ex plicit algo- rithm refuting the conjecture. Concretely we can factorize an RSA ...
• #### Square-free discriminants of Frobenius rings ﻿

(2010-09)
Article
Accés obert
Let E be an elliptic curve over Q. It is well known that the ring of endomorphisms of $E_p$, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field $Q(\pi_p)$ generated ...